In this paper, we propose two compact quantum circuits to implement post-selected CPF gate and Toffoli gate in the coincidence basis using solely polarizing beam splitters (PBSs), half-wave plates (HWPs), beam splitters (BSs), and single-photon detectors.
Assisted by one and two independent single photons, our CPF and Toffoli gates are accomplished respectively when exactly one photon appears in each output mode.
Our schemes are appealing for higher success probabilities and less quantum resource requirements.
The existing highest success probability of a linear optical CPF gate 1/4 is achieved resorting to an auxiliary single photon in our scheme rather than an auxiliary entangled photon pair [1]}, [2]}, [3]}, [4]}, [5]}.
The presented CPF gate also beats the ones with the success probability of 1/8 assisted by two single photons [6]}, [7]}, and the ones with 1/9 without auxiliary photons [8]}, [9]}, [10]}, [11]}, [12]}, [13]}.
In addition, the average success probability of our Toffoli gate is high to 1/30, which far exceeds all previous results for the same works [14]}, [15]}, [16]}, [17]}.
